Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum

Abstract

We construct a Lipschitz function on R2 which is locally convex on the complement of some totally disconnected compact set but not convex. Existence of such function disproves a theorem that appeared in a paper by L.

Pasqualini and was also cited by other authors.

Keywords

• convex function
• convex set
• exceptional set